FYI, I've had no problem letting Claude code read iMessage and send iMessage from my Mac logged into iCloud. The first time you ask it to do that, macOS will throw up a security prompt asking for permission for Terminal.app to access the data, but its something I've been using a lot recently.
Apps can integrate into iMessage, there's an API. You're thinking of sending and receiving actual iMessage messages as a full user, which they can't do.